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Chinese Physics Letters

Implementation of Quantum Logic Gates by Nuclear Magnetic Resonance Spectroscopy

Jiangfeng Du, Jihui Wu, Ming-Jun Shi, Liang Han, Xianyi Zhou, Bangjiao Ye, Huiming Weng, Rongdian Han

Published Jan 1, 2000• 10 citations
Publisher

Abstract

Using nuclear magnetic resonance techniques with a solution of cytosine molecules, we show an implementation of certain quantum logic gates (including NOT gate, square-root of NOT gate and controlled-NOT gate), which have central importance in quantum computing. In addition, experimental results show that nuclear magnetic resonance spectroscopy can efficiently measure the result of quantum computing without attendant wave-function collapse.

DOI
10.1088/0256-307x/17/1/022

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Using nuclear magnetic resonance techniques with a solution of cytosine molecules, we show an implementation of certain quantum logic gates (including NOT gate, square-root of NOT gate and controlled-NOT gate), which have central importance in quantum computing. In addition, experimental results show that nuclear magnetic resonance spectroscopy can efficiently measure the result of quantum computing without attendant wave-function collapse.
Quantum computing shows great promise for the solution of many difficult problems, such as the simulation of quantum systems and the factorization of large numbers. While the theory of quantum computing is fairly well understood, it has proved difficult to implement quantum computers in real physical systems. It has recently been shown that nuclear magnetic resonance (NMR) can be used to implement small quantum computers using the spin states of nuclei in carefully chosen small molecules. Here we demonstrate the use of a NMR quantum computer based on the pyrimidine base cytosine, and the implementation of a quantum algorithm to solve Deutsch’s problem (distinguishing between constant and balanced functions). This is the first successful implementation of a quantum algorithm on any physical system.
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We consider two new quantum gate mechanisms based on nuclear spins in hyperpolarized solid 129Xe^{129}Xe129Xe and HCl mixtures and inorganic semiconductors. We propose two schemes for implementing a controlled NOT (CNOT) gate based on nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI) from hyperpolarized solid 129Xe^{129}Xe129Xe and HCl mixtures and optically pumped NMR in semiconductors. Such gates might be built up with particular spins addressable based on MRI techniques and optical pumping and optical detection techniques. The schemes could be useful for implementing actual quantum computers in terms of a cellular automata architecture.
We discuss the applications of Nuclear Magnetic Resonance (NMR) to quantum information processing, focusing on the use of quadrupole nuclei for quantum computing. Various examples of experimental implementation of logic gates are given and compared to calculated NMR spectra and their respective density matrices. The technique of Quantum State Tomography for quadrupole nuclei is briefly described, and examples of measured density matrices in a two-qubit I = 3/2 spin system are shown. Experimental results of density matrices representing pseudo-Bell states are given, and an analysis of the entropy of theses states is made. Considering an NMR experiment as a depolarization quantum channel we calculate the entanglement fidelity and discuss the criteria for entanglement in liquid state NMR quantum information. A brief discussion on the perspectives for NMR quantum computing is presented at the end.
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In this article we consider nuclear magnetic resonance (NMR) as an example of a quantum technology; we consider in particular detail the implementation of quantum computers using NMR. We begin by outlining the physical principles underlying NMR, and give an introduction to the quantum mechanics involved. We next discuss the general characteristics of quantum technologies and the ways and extent to which these characteristics are expressed in NMR. We then give an introduction to the subject of quantum computation and its implementation using NMR. Finally, we describe some spectroscopy techniques which also exploit the quantum nature of NMR.